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aluminum metal can be recycled from scrap metal by melting the metal to evaporate impurities calculate the amount of heat needed to purify one mole of aluminum originally at 298 Kelvin by melting it the melting point of aluminum is 933 Kelvin the molar heat capacity of aluminum is 24 joules per mole Kelvin and the heat of fusion of aluminium is 10 point 7 kilojoules per mole all right so we don't think about the heat they needed to raise its temperature from 298 Kelvin to raise the temperature of this one mole of aluminum from 298 Kelvin to 933 Kelvin and we're going to do that by looking at the molar heat capacity and then we need to add to that the heat of fusion the heat necessary to actually melt it so let's do that in steps so heat heat needed heat needed to raise temperature sure by how many how many how much we are raising the temperature by we're going from 298 to 933 so see if you're raised by 2 you get to 300 and then you have to raise by another 633 so that's going to be so we're raising our temperature by 635 Kelvin that's to get it to the melting point so the heat needed to raise temperature by 635 Kelvin well we have we have one mole one mole of aluminum I can write 1.0 o to show that we have two significant dujour three significant digits there one mole of aluminum times the specific or the molar heat capacity I should say so 24 joules per mole per mole Kelvin times so this right over here would be the amount of heat to raise it by one Kelvin but now let's multiply by we have to raise it by 635 Kelvin 635 Kelvin and the units work out moles cancel with moles Kelvin cancels with cancels Kelvin cancels with Kelvin and then we get to let's see we get my calculator out here so 24 times 635 is equal to 15,000 240 and are we're taking the product of a bunch of stuff three significant figures two significant figures three significant figures so we should only we should write only two significant figures so we'll round to 15,000 joules so this is going to be fifteen fifteen thousand joules just to raise the temperature to 933 Kelvin and then we have the heat heat of fusion heat to melt once at melting point melting point well that is going to be one mole one mole times the heat of fusion times ten point seven kilojoules kilojoules per mole so this is going to give us ten point seven kilojoules or if we want to write it in joules so this is ten point seven kilojoules which is equal to ten thousand seven hundred joules and so the total the total is going to be the sum of these so we could say it is twenty five thousand seven hundred but we only have two significant figures here so we could round that and so we could say twenty six thousand twenty-six thousand joules or I guess we could write two twenty six twenty six kilojoules all right now Part B Part B the equation for the overall process of extracting aluminum from aluminum oxide is shown below alright shown below which which requires less energy recycling a little existing aluminum or extracting aluminum from aluminum oxide justify your answer with a calculation alright so this reaction this reaction right over here if and this is this gives us the the heat sorry for a mole of the reaction so if you get a mole of aluminum oxide you put in this much heat you're going to get two moles of aluminum and 1.5 moles of molecular oxygen so the equation the so let's see the equation for the overall process so to extract to extract one mole one mole of aluminum from aluminum oxide requires so this much heat will produce 2 moles so to do one mole you just have to have half of that requires 1675 kilojoules divided by 2 so this is going to be 1675 divided by 2 is equal to let's see it's going to be eight hundred thirty seven point five eight hundred thirty seven point five eight hundred thirty seven point five kilojoules you know that's half here and had four significant digits here and I still have four significant digits extracting doing it from which requires less recycling existing aluminum or extracting it well to to recycle one mole requires we just figure it out twenty six kilojoules twenty six kilojoules everything here's some Quilt kilojoules which is much less energy which is much less energy and we are done
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